Effect of magnetic anisotropy on direct chiral discrimination in paramagnetic NMR spectroscopy

We present and analyse a complete analytic expression for the generalized shielding polarizability third-rank tensorΦαβγ, whose isotropic average, the pseudoscalar, is proportional to a chiral macroscopic electric polarization P measurable in a pulsed nuclear magnetic resonance (NMR) experiment probing molecules with an arbitrarily degenerate ground state, in solution. We have recently predicted that can be measurable at room temperature in chiral paramagnetic molecules, and identified strong magnetic anistropy (as featurede.g.in lanthanide complexes) as a crucial molecular property to achieve room temperature chiral discrimination using NMR spectroscopy. As previously proposed, the components ofΦαβγare obtained as analytical third derivatives of the electronic free energy. Here we present the explicit calculation of these derivatives, which provide working expressions for the explicit accurateab initiocalculation ofΦαβγ. We apply our theory by performingab initiomulticonfigurational calculations of all contributions toΦαβγ, for a set of ten DyIIIcomplexes, characterized by a strongly axial ground Kramers doublet, but also by thermally accessible excited Kramers doublets at room temperature. The results show that the thermally populated excited state contributions, while generally reducing the value of calculated on the assumption of a thermally isolated ground state, still confirm the room temperature detectability of this property for all ten studied complexes. Trends on the relative sign of dominant contributions are then discussed on the basis of a crystal field model electrostatic potential splitting a ground spin-orbit multiplet, which provides an insight into the properties of the generalized shielding polarizability tensor for open shell species.